Question

Suppose refractive index $\mu$ is given as $\mu = A + \frac{B}{\lambda^2}$ where A and B are constants and $\lambda$ is wavelength, then dimensions of B are same as that of

• A. wavelength
• B. volume
• C. pressure
• D. area

Answer 1

Answer: (D)

area

Answer 2

$\mu = \frac { velocity \, of \, light \, in \, vacuum }{ velocity \, of \, light \, in \, medium }$
The refractive index $\mu$ is dimensionless, so each term on right hand side is dimensionless. Hence, $\frac{ B }{ \lambda^2 }$ is dimensionless.
This implies that dimensions of B will have the dimensions of
$\lambda^2$ ie, of area. ie, of $cm^2$ or area.